MathDB

A four-digit positive integer is called virtual if it has the form

\overline{abab}

, where

a

and

b

are digits and

a \neq 0

. For example 2020, 2121 and 2222 are virtual numbers, while 2002 and 0202 are not. Find all virtual numbers of the form

n^2+1

, for some positive integer

n

Problem Statement